Question

3) If A x: xis a factors of 72
B- x:x is a multiple of 4 is smaller than 41
Find {A-B) U (BA)​

Answer 1

• (A - B) U (B - A) = {1, 2, 3, 5, 6, 9, 16, 18, 20, 28, 32, 40, 72}
• (A - B) U (A ∩ B) = {1, 2, 3, 5, 6, 8, 9, 12, 18, 24, 36, 72}

Step-by-step explanation:

Given,

A = {x | x is a factor of 72}

= {1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72}

B = {x | x is a multiple of 4, x < 41}

= {4, 8, 12, 16, 20, 24, 28, 32, 36, 40}

Then,

A - B = {x | x ∈ A but x ∉ B}

= {1, 2, 3, 5, 6, 9, 18, 72}

B - A = {x | x ∈ B but x ∉ A}

= {16, 20, 28, 32, 40}

A ∩ B = {x | x ∈ A and x ∈ B}

= {4, 8, 12, 24, 36}

Now, (A - B) U (B - A)

= {x | x ∈ (A - B) or x ∈ (B - A)}

= {1, 2, 3, 5, 6, 9, 16, 18, 20, 28, 32, 40, 72}

and (A - B) U (A ∩ B)

= {x | x ∈ (A - B) or x ∈ (A ∩ B)}

= {1, 2, 3, 5, 6, 8, 9, 12, 18, 24, 36, 72}